The present invention relates to a work spindle head for a machine tool spindle, especially a milling head for a milling spindle, comprising torque motors to rotate the spindle around at least two different axes. In addition, the present invention relates to a milling machine which is equipped with this type of milling head and constructed with portal design. Such portal milling machines are frequently used for toolmaking, mold making and model making or production in the automotive, aviation and space industries and in other applications in which complex surfaces must be configured on large tools with extremely high surface quality and processing speed.